k/t gallows reduplication

[nablator]

I don't remember reading about how the k/t gallows sequence compares to random and human-generated pseudo-random sequences. It is likely that I missed something, so please point me to any existing analysis.

There is a blog post by Emma May Smith but it does not discuss the reduplication statistics: You are not allowed to view links. Register or Login to view.

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TLDR: The k/t gallows sequence is strongly biased toward reduplication; especially long sequences of the same k/t gallows in a row.

What is interesting about it is that human-generated pseudo-random sequences have a "tendency to overalternate between outcomes" documented in psychology studies. See for example: You are not allowed to view links. Register or Login to view. and the referenced literature.

Why do we see the opposite tendency in the VMS?

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EVA-k is more frequent than EVA-t. In the ZL transliteration, in paragraphs only, there are:
k = 10096, probability(k) = pk = 62%
t = 6063, probability(t) = pt = 38%
In few cases of ambiguity, I kept the first: for example [k:t] = k.

With perfectly random independent draws, in any window of n letters of the k/t sequence, the probability of having:
n times k is pk^n
n times t is pt^n
The expected number of windows of n identical letters in the k/t sequence is the probability multiplied by the number of windows:
For k: (k+t-n+1)*pk^n
For t: (k+t-n+1)*pt^n

The expected numbers are ek, et (rounded), the actual numbers are ak, at:
n    ek  <  ak      et  <  at 
2  6307   6956    2274   2924
3  3940   4938     853   1554
4  2461   3593     320    870
5  1538   2686     120    501
6   960   2029      45    300
7   600   1565      16    184
8   375   1214       6    117
9   234    950       2     76
10  146    752       0     50
11   91    595       0     32
12   57    465       0     21

Note: if you count kk... and tt... sequences with a text editor like Notepad++, the numbers will be lower, because it skips to the text following the matched pattern instead of doing a "rolling window" search.

[nablator]

I am looking more closely to find the longest sequences of k and t in paragraphs.

You are not allowed to view links. Register or Login to view. has a lot of k: 40 or 41 in a row at the end, if the last one is not a label:
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In You are not allowed to view links. Register or Login to view. the first paragraph has a lot of t, the second paragraph has a lot of k.
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Cluster of k in f90r2:
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It is possible that clusters explain the long sequences, mostly.

[MarcoP]

Hi Nablator,
if I understand correctly, when you refer to sequences and reduplication, you are ignoring everything that isn't either 'k' or 't' .  E.g. this counts as a triple reduplication of 't', because 3 't's occur with no 'k' between them:

<f3r.14,+P0>      chor.qodair.okeey.qokeey<$>
<f3r.15,+P0>      <%>tsheoarom.shor.or.chor.olchsy.chom.otchom.<->oporar
<f3r.16,+P0>      oteol.chol.s.cheol.ekshy.qokeom.qokol.daiin.<->soleeg

I guess that 'k' sequences are partly explained by the fact that 'k' is much more frequent than 't' in Currier B.
But, in Currier A, 't' and 'k' have similar frequencies, so one doesn't expect many long sequences of 't' in any of the two languages.

I would say that your You are not allowed to view links. Register or Login to view. link (Currier A) is a good illustration for the kind of sequences you pointed out.

[nablator]

I guess that 'k' sequences are partly explained by the fact that 'k' is much more frequent than 't' in Currier B.

Hi MarcoP,

I'll do the calculation for Currier A and Currier B separately, then page per page. Maybe the large imbalance of the k:t ratio on some page is enough to explain most of the long sequences.

It's as if they tried to compensate the lesser frequency of t with longer sequences of t than k. Just an idea, I don't know.

[nablator]

Currier B behaves differently than Currier A as usual.

[MarcoP]

Since long t-sequences in Currier B appear to be particularly unexpected, I had a look at some of the longest.

One starts at the end of f85r1 (the script I used ignores page boundaries) and goes on on the outer circular text of f85r2. The four sections inside the circle are also quite interesting: Top and Right are mixed, bottom is 't' only and right is 'k' only.
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The second one also is a circular text (f86v4):
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I guess that the previous two sequences are not counted in Nablator's numbers, which are based on paragraph text.

Another sequence is from the right-hand side of the adjacent f86v3 (which is not circular, but still has a layout that goes around the page)
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Other two long t-sequences appear in f114v, at the top of the page and at line 11 (4th star).
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While Quire20 in general shows a strong preference for 'k' over 't', You are not allowed to view links. Register or Login to view. is an exception where the preference is opposite.

[nablator]

(k-t)/(k+t), this time from the entire TT transliteration.

[R. Sale]

Can someone color code that for the different hands/scribes?

[nablator]

Can someone color code that for the different hands/scribes?

The sequential diagram shows that dots are very scattered in every section, so there is no correlation. Q13 is entirely in the k>t area, though.

[ReneZ]

(k-t)/(k+t), this time from the entire TT transliteration.

Out of curiosity, and no criticism implied: what exactly do you mean with "TT transliteration" ?